Algorithm For Economic Dispatch Research Articles

A distributed consensus based algorithm for economic dispatch over time‐varying digraphs

AbstractIn this paper, a consensus based fully distributed optimization algorithm is proposed for solving economic dispatch problem (EDP) in smart grid. Since the incremental cost of all buses reach consensus when the optimal solution is achieved, it is selected as a consensus variable. An additional variable at each bus, called “surplus” is added to record the local power mismatch, which is used as a feedback variable to purse the balance between power supply and demand. Different from most of the existing distributed methods which require the communication network to be balanced, the algorithm uses a row random matrix and a column random matrix to precisely steer all the agents to asymptotically converge to a global optimal solution over a time‐varying directed communication network. Due to the use of a fixed step size, the proposed algorithm also outperforms other algorithms in terms of convergence speed. The graph and eigenvalue perturbation theories are employed for the algorithm convergence analysis, and the upper bound of the parameters required for convergence is given theoretically. Finally, the performance and scalability of the proposed distributed algorithm are verified by several case studies conducted on the IEEE 14‐bus power system and a 200‐node test system.

Chaos Moth Flame Algorithm for Multi-Objective Dynamic Economic Dispatch Integrating with Plug-In Electric Vehicles

Dynamic economic dispatch (DED) plays an important role in the operation and control of power systems. The integration of DED with space and time makes it a complex and challenging problem in optimal decision making. By connecting plug-in electric vehicles (PEVs) to the grid (V2G), the fluctuations in the grid can be mitigated, and the benefits of balancing peaks and filling valleys can be realized. However, the complexity of DED has increased with the emergence of the penetration of plug-in electric vehicles. This paper proposes a model that takes into account the day-ahead, hourly-based scheduling of power systems and the impact of PEVs. To solve the model, an improved chaos moth flame optimization algorithm (CMFO) is introduced. This algorithm has a faster convergence rate and better global optimization capabilities due to the incorporation of chaotic mapping. The feasibility of the proposed CMFO is validated through numerical experiments on benchmark functions and various generation units of different sizes. The results demonstrate the superiority of CMFO compared with other commonly used swarm intelligence algorithms.

Projection-based distributed economic dispatch algorithm considering communication delays under switching topologies

In this paper, a projection-based distributed algorithm is proposed to solve the economic dispatch problem of power system with communication delays under switching topologies. The algorithm is suitable for economic dispatch problem with strongly convex cost function, and ensures that the output power of each generator is always kept within its output limit. In addition, the topology is only required to be jointly connected. Firstly, the relationship between the equilibrium point and the optimal solution of the algorithm is analyzed, and then a common Lyapunov function is introduced for a set of switching topologies. According to the Lyapunov stability theory and Cauchy convergence criterion, LMIs-based sufficient conditions for the convergence of the algorithm are obtained. Finally, the effectiveness of the algorithm under different cases are verified by MATLAB simulation results.

A scalable graph reinforcement learning algorithm based stochastic dynamic dispatch of power system under high penetration of renewable energy

Due to the increasing penetration of renewable energy source, power system is facing significant uncertainties. How to fully consider those uncertainties in dynamic economic dispatch (DED) has become a crucial problem to the safe and economic operation of power system. Reinforcement learning (RL) based approaches can provide the dispatch policy in response to uncertainty. However, current RL uses traditional Euclidean data representation, which greatly reduces the scalability and computational efficiency of economic dispatch algorithms. To address such obstacle, this paper develops a novel graph reinforcement learning (GRL) method for DED of power system. Firstly, DED is formulated as a Markov decision process and formulated as a dynamic sequential decision problem. Secondly, a novel graph-based representation of system state is proposed. Using graph data to represent dispatch operation data with non-Euclidean characteristics can effectively capture the implicit correlation of the uncertainty corresponding to the system topology. Thirdly, a GRL algorithm is proposed to learn the optimal policy which maps graph represented system state to DED decision. Compared with the traditional deep reinforcement learning (DRL), the GRL proposed in this paper has certain generalization ability and scalability, and can achieve higher quality solutions in online operation. Case studies illustrate that the optimality of the proposed method is 98.04%, which is 15.13% higher than that of the existing learning methods. The algorithm is scalable and improves the sample efficiency.

Distributed algorithm for economic dispatch with transmission losses under digraph

By taking transmission losses and directed communication into considered, a more practical scenario of economic dispatch problem is studied in the paper. It is formulated as a non-convex optimization problem. Using convex relaxation, the non-convex optimization problem is transformed into convex optimization problem, and the conditions to ensure that they have the same solution are given. Then, a consensus-based distributed algorithm with time-varying feedback gains is presented, which can be used to the general directed communication networks. Especially, the convergence and optimality of the proposed algorithm are proved by using multi-parameter eigenvalue perturbation theory and graph theory. Finally, simulation results validate the theoretical results and illustrate the effectiveness and advantages of the proposed algorithm.

An elitist cuckoo search algorithm for combined heat and power economic dispatch

Combined heat and power economic dispatch (CHPED) is one of the foremost subjects in the operation of power systems. In this article, a new variant of cuckoo search (CS) algorithm, elitist CS (yECS), is advanced to tackle CHPED. During the optimisation process of the original CS as well as lots of its variants, the guidance of search directions relies merely upon the best individual, causing the loss of other beneficial information and further influencing their performance potentials. Therefore, in yECS, an elitist mechanism is developed to fully utilise the beneficial information of other elite individuals. Specifically, three new iterative strategies are developed, one for the global search phase and the other two for the local search phase. Further, a coordinated mechanism is put forward to effectively integrate the local iterative strategies, thus helping yECS in maintaining an appropriate balance between exploitation and exploration. The superior performance of yECS is firstly substantiated via CEC 2017 test suite and two engineering design problems and then it is utilised to address CHPED problems. All optimal dispatch results acquired by yECS are feasible and in most cases display remarkable improvements over the results determined by other CS variants and some recently-published literature results.

A Surrogate-Assisted Adaptive Bat Algorithm for Large-Scale Economic Dispatch

Large-scale grids have gradually become the dominant trend in power systems, which has increased the importance of solving the challenges associated with large-scale economic dispatch (LED). An increase in the number of decision variables enlarges the search-space scale in LED. In addition to increasing the difficulty of solving algorithms, huge amounts of computing resources are consumed. To overcome this problem, we proposed a surrogate-assisted adaptive bat algorithm (GARCBA). On the one hand, to reduce the execution time of LED problems, we proposed a generalized regression neural network surrogate model based on a self-adaptive “minimizing the predictor” sampling strategy, which replaces the original fuel cost functions with a shorter computing time. On the other hand, we also proposed an improved hybrid bat algorithm (RCBA) named GARCBA to execute LED optimization problems. Specifically, we developed an evolutionary state evaluation (ESE) method to increase the performance of the original RCBA. Moreover, we introduced the ESE to analyze the population distribution, fitness, and effective radius of the random black hole in the original RCBA. We achieved a substantial improvement in computational time, accuracy, and convergence when using the GARCBA to solve LED problems, and we demonstrated this method’s effectiveness with three sets of simulations.

Privacy masking distributed saddle-point algorithm for dynamic economic dispatch

Privacy masking distributed saddle-point algorithm for dynamic economic dispatch

A DRO-SDDP Decentralized Algorithm for Economic Dispatch of Multi Microgrids With Uncertainties

A DRO-SDDP Decentralized Algorithm for Economic Dispatch of Multi Microgrids With Uncertainties

Model-Free Reinforcement Learning Economic Dispatch Algorithms for Price-Based Residential Demand Response Management System

Model-Free Reinforcement Learning Economic Dispatch Algorithms for Price-Based Residential Demand Response Management System

Distributed Economic Dispatch for Microgrids Tracking Ramp Power Commands

When in grid-connected mode of operation, distributed generators (DGs) within the microgrid (MG) can coordinate to act as a single entity to provide services to the bulk grid. The DGs can coordinate their power production to minimize the total operating cost, which is known as the distributed economic dispatch. Various methods have been proposed to solve the MG economic dispatch problem (EDP) in a distributed fashion, under the assumption that DGs’ power output, in aggregate, follows a constant or slowly varying power command. However, when the MG is providing frequency regulation service, or the internal load is highly dynamic, the MG EDP becomes dynamic, and the state-of-the-art distributed approaches cannot guarantee optimality. In this paper, we propose a distributed economic dispatch algorithm for MGs providing frequency regulation service, as an example of a dispatch profile with ramp commands. A consensus protocol guaranteeing zero steady-state error for ramp inputs is integrated into the EDP to find the optimal solution in a distributed way. With the proposed algorithm, the MG is able to tightly follow a time-varying regulation signal while maintaining an optimal economic dispatch for all the DGs within. We validate the proposed method using regulation signals from PJM and demonstrate the algorithm on a hardware-in-the-loop testbed.

An Improved Artificial Ecosystem Algorithm for Economic Dispatch with Combined Heat and Power Units

The most effective use of numerous Combined Heat and Power Units (CHPUs) is a challenging issue that requires strong approaches to handle the Economic Dispatch (ED) with CHPUs. It aims at minimizing the fuel costs by managing the Power-Only Units (POUs), CHPUs, and Heat-Only Units (HOUs). The transmission losses are also integrated, which increases the non-convexity of the ED problem. This paper proposes a Modified Artificial Ecosystem Algorithm (MAEA) motivated by three energy transfer processes in an ecosystem: production, consumption, and decomposition. The MAEA incorporates a Fitness Distance Balance Model (FDBM) with the basic AEA to improve the quality of the solution in non-linear and multivariate optimization environments. The FDBM is a selection approach meant to find individuals which will provide the most to the searching pathways within a population as part of a reliable and productive approach. Consequently, the diversity and intensification processes are carried out in a balanced manner. The basic AEA and the proposed MAEA are performed, in a comparative manner considering the 7-unit and 48-unit test systems. According to numerical data, the proposed MAEA shows a robustness improvement of 97.31% and 96.63% for the 7-unit system and 46.03% and 60.57% for the 48-unit system, with and without the power losses, respectively. On the side of convergence, based on the average statistics, the proposed MAEA shows a considerable improvement of 47% and 43% of the total number of iterations for the 7-unit system and 13% and 20% of the total number of iterations for the 48-unit system, with and without the power losses, respectively. Thus, the suggested MAEA provides significant improvements in the robustness and convergence properties. The proposed MAEA also provides superior performance compared with different reported results, which indicates a promising solution methodology based on the proposed MAEA.

Event-triggered scheme for finite-time distributed economic dispatch in smart grids

This paper considers the finite-time distributed economic dispatch problem in smart grids: the power generated by individual generators are designed to satisfy a certain demand while minimizing the total generation cost in a distributed manner, which guarantees the convergence in finite time. The proposed method facilitates the solution of real time power dispatch problems. First, a class of distributed economic dispatch algorithm is proposed to achieve the optimal solution in finite-time with and without capacity limitations. Second, in order to reduce the information exchange requirements, a distributed, asynchronous event-triggered communication scheme is established which is free of Zeno with guaranteed finite-time convergence. Furthermore, both proposed algorithms are robust to the time-varying communication networks. Simulation results illustrate the effectiveness and scalability of the distributed algorithms.

Dispatch-aware planning for feasible power system operation

Maintaining stable energy production with increasing penetration of variable renewable energy requires sufficient flexible generation resources and dispatch algorithms that accommodate renewables’ uncertainty. In this work, we study the feasibility properties of real-time economic dispatch (RTED) algorithms and establish fundamental limits on their performance. We propose a joint methodology for resource procurement and online economic dispatch with guaranteed feasibility. Our algorithm, Feasible Fixed Horizon Control (FFHC) is a regularized form of Receding Horizon Control (RHC) that balances exploitation of good near-term demand predictions with feasibility requirements. Empirical evaluation of FFHC in comparison to the standard RHC on realistic load profiles highlights that FFHC achieves near-optimal performance while ensuring feasibility in high-ramp scenarios where RHC becomes infeasible. • Increasing variability of net demand requires dispatch-aware power system planning. • Offline planning is insufficient to ensure online dispatch feasibility. • Feasible planning algorithm uses affine feedback policies to approximate dispatch. • Online economic dispatch algorithm adapts standard receding horizon control. • Joint algorithm achieves guaranteed feasibility with near-optimal dispatch efficiency.

Scenario-oriented hybrid particle swarm optimization algorithm for robust economic dispatch of power system with wind power

An economic dispatch problem for power system with wind power is discussed. Using discrete scenario to describe uncertain wind powers, a threshold is given to identify bad scenario set. The bad-scenario-set robust economic dispatch model is established to minimize the total penalties on bad scenarios. A specialized hybrid particle swarm optimization (PSO) algorithm is developed through hybridizing simulated annealing (SA) operators. The SA operators are performed according to a scenario-oriented adaptive search rule in a neighborhood which is constructed based on the unit commitment constraints. Finally, an experiment is conducted. The computational results show that the developed algorithm outperforms the existing algorithms.

Distributed Economic Dispatch Control Method with Frequency Regulator for Smart Grid under Time-Varying Directed Topology

The paper studies a new distributed control method to solve the economic dispatch problem (EDP) under directed topology based on consensus protocol. Electrical equipment is closely related to frequency, and the frequency of each generator varies independently during operation. Therefore, it hinders the realization of economic dispatch. To solve the problem, we combine a frequency regulator with a consensus protocol, which eliminates the effect of frequency variation on the designed consensus algorithm. Meanwhile, considering the problem of excessive communication cost and low computational efficiency in large-scale power systems, an event-triggered mechanism is introduced into the designed algorithm. Furthermore, in order to overcome the unexpected loss of communication links, the time-varying topology mechanism is employed to develop the distributed economic dispatch (DED) algorithm to improve the robustness. Then, the stability of the above algorithm is proved by graph theory and convergence analysis. Finally, several simulations illustrate that our proposed methods are effective.

An efficient distributed algorithm for economic dispatch considering communication asynchrony and time delays

The increasing integration of distributed energy resources (DERs) to power grids has fostered the emergence of advanced control technologies for energy management. This study focuses on distributed solutions to economic dispatch considering asynchrony and non-ideal communications. A distributed consensus-based algorithm is developed for general directed networks, where heavy-ball momentum is incorporated into the algorithm design to accelerate convergency. Subsequently, an asynchronous version is proposed based on a general asynchronous communication model with unpredictable, non-uniform, and bounded time delays. Without a global clock in conventional synchronous distributed algorithms, distributed generators (DGs) are allowed to exchange information through local communications at any moment and use out-sync information to execute new updates. Simulations are presented to demonstrate the performance of the proposed algorithm and verify its robustness against time delays.

Improved approximate dynamic programming for real-time economic dispatch of integrated microgrids

Economic dispatch of electricity-heat microgrid is critical for real-time power generation and storage. However, conventional economic dispatch algorithms are generally integrated with static unit models without considering dynamics of units, thus leading to difficulties for real deployment in stochastical environments. In this paper, we propose a novel approximate dynamic programming (ADP) based real-time optimization algorithm. Specifically, the proposed ADP is employed to solve the Markov decision process with considering the dynamic process of combined-cycle gas turbine. Furthermore, we also design a novel weighted piecewise linear function to achieve the near-optimal solution, which is simple but effective for computational complexity reduction. In the experimental section, we conduct extensive experiments with comparisons to other economic dispatch methods. The experimental results indicate that: 1) The dynamic process of energy conversion brings more practical solutions; 2) The proposed ADP-based method could handle the stochasticity of the microgrid; 3) The proposed method outperforms the other intra-day optimization policies in both economical and computational efficiency.

Distributed Economic Dispatch Based on Finite-Time Double-Consensus Algorithm of Integrated Energy System

To reduce the operating cost and enhance the energy utilization efficiency of the integrated energy system (IES), an economic dispatch algorithm is proposed based on finite-time double-consensus. First, an economic dispatch model of IES under two modes of operation, islanded and grid-connected, is constructed considering energy transmission losses. After that, the optimal improved incremental cost and power output allocation of the IES can be found out in finite time. The proposed algorithm contains two finite-time consistency protocols simultaneously that can solve the optimal values of the incremental cost of electricity and heat of integrated energy system, solving the strong coupling problem of multi-energy systems. The proposed algorithm not only has a faster convergence rate but also enables switching freely between the two operation modes. In addition, a distributed method for quickly discovering the total system power mismatch is proposed in the process of algorithm solving. The finite-time convergence of the proposed algorithm is demonstrated. Finally, the IES simulation based on the IEEE 30-node power system and the Bali 32-node thermal system is established. The analysis of the simulation results shows that the algorithm proposed in this paper is effective.

A hunger game search algorithm for economic load dispatch

This work proposes a new approach to solve the economic load dispatch (ELD) issue in power systems by metaheuristic algorithms inspired by natural life. The problem to be resolved is to optimize the power system network with various constraints by considering the cutting in the cost of the resulting in the transmission of the electric system. The method used in this study is the hunger games search (HGS). This method duplicates the hungerdriven activity and the animal's choice of behavior. The proposed method is to add the concept of starvation as a process structure. Adaptive weights based on the concept of hunger are designed and used to simulate the effects of hunger on each trace process. To get the performance of the proposed method, this research uses mathematical methods, particle swarm optimization (PSO), differential evolution (DE), giza pyramids construction (GPC), and sine tree-seed algorithm (STSA) as a comparison. This study uses 2 case studies. In case study 1, the proposed method has a 0.16% better cost of generation than the mathematical method. Comparison of the HGS method with the PSO method in the second case study, it was found that the HGS method was 0.018% better than the PSO. From the research, it was found that the HGS method was superior.